Sean Price, 32, pleaded guilty to murder, rape, robbery and attempted theft after a crime spree in March 2015.
He killed the 17-year-old schoolgirl while she was on her evening walk, and told police he then raped a woman because he knew he was going to jail forever.
Price has now applied to Victorian Legal Aid for funding to appeal the conviction.
Senator Derryn Hinch called the request "an absolute disgrace".
"This man, he deserves to spend every one of those 38 years in jail," Mr Hinch said.
"He stabbed that teenage girl in that park 47 times. Legal Aid Victoria should not give this monster one single solitary dollar."
Masa's boyfriend at the time she was killed, Tim Draper, said the legal system was flawed.
"It's appalling that a person who committed such atrocities is allowed to take advantage of the system.
"Unfortunately the Australian government and the legal system let it go on and that shows how broken the system is."
Legal aid is considering if it would fund Price's appeal. A VLA spokesperson said everyone is entitled to apply for legal assistance and Price's application would be assessed the same as that of any other Victorian's
Price would have to meet specific criteria and community outrage would not sway its decision, the spokesperson said.
"The attorney-general is prohibited from interfering in any decision about an individual, and the views and attitudes about applicants are similarly not relevant under our system of justice," a VLA spokesman said in a statement.
"Sometimes those applications are granted and sometimes they are not. Our obligation is to assess those applications with fairness and impartiality."
Premier Daniel Andrews said Price is in jail "exactly where he should be" but the government would not intervene in the legal aid process.
"There is a process and it's not for politicians to trample on that process, or to seek to run it," Mr Andrews said on Tuesday.
"I think that an independent legal aid assessment process is very important."
Price's application has outraged the Victims of Crime Commission, which says the victims' human rights are being ignored.
"He's been charged, tried, convicted and sentenced all on the public purse. Surely you only get one go, don't you?" Victims of Crime commissioner Greg Davies said.
"Almost everyone forgets the victims but they're taxpayers too, and he wants taxpayers' money."
The state opposition called Price a "monster" and called on the premier intervene.
"Daniel Andrews can intervene to ensure this monster cannot continue to draw on Victoria's taxpayers," shadow attorney-general John Pesutto said.
"An appeal just adds to the trauma that the victims have already suffered."
'Absolute disgrace': Outrage over Masa Vukotic's killer seeking legal aid to fund rape conviction appeal Yahoo and Agencies
Brutal stabbing murder of Masa Vukotic sparks tough new laws in Victoria for violent sex offenders who can now be held for up to 72 hours without charge John Carney Daniel Peters Daily Mail Australia and Aap 22 March 2016